Properties

AuxiliaryLevel(M) : ModSS -> RngIntElt

The level of M, where the auxiliary level of SupersingularModule(p,N) is, by definition, N.

BaseRing(M) : ModSS -> Rng

The base ring of M. (Currently this is always Z.)

Degree(P) : ModSSElt -> RngElt

The sum of the coefficients of P, where P is written with respect the basis of the ambient space of the parent of M.

Dimension(M) : ModSS -> RngIntElt

The dimension of M.

Eltseq(P) : ModSSElt -> SeqEnum

A sequence of integers that defines P.

Level(M) : ModSS -> RngIntElt

The level of M, where the level of SupersingularModule(p,N) is, by definition, Np.

ModularPolynomial(M) : ModSS -> RngMPolElt

The defining polynomial of X_0(N) that we use to compute the module of supersingular points.

Prime(M) : ModSS -> RngIntElt

The prime of M, where the prime of SupersingularModule(p,N) is, by definition, p.

Example ModSS_Properties (H92E4)

> M := SupersingularModule(3,11);
> AuxiliaryLevel(M);
11
> BaseRing(M);
Integer Ring
> Degree(M.1+7*M.2);
8
> Dimension(M);
2
> Eltseq(M.1+7*M.2);
[ 1, 7 ]
> Level(M);
33
> Prime(M);
3
> M := SupersingularModule(11,3); M;
Supersingular module associated to X_0(3)/GF(11) of dimension 4
> ModularPolynomial(M);
x*y + 8